Author

Mahbod Majid

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Preprint Sep 2026

Subexponential Approximation of the Permanent in Deterministic Polynomial Time

We give the first deterministic polynomial time algorithm that approximates the permanent of arbitrary nonnegative rational matrices within a subexponential factor. For a matrix of order $n$, the approximation factor is \[ \exp\!\left(O\!\left(\frac{n(\log\log n)^2}{\log n}\right)\right)=\exp(o(n)). \] All previously k...

S. Kudria, Jason Luo, Mahbod Majid · 2 citations

#machine learning Preprint Sep 2026

Tight Lower Bounds for State Tomography with Limited Entanglement

We study state tomography when each measurement acts on at most $k$ fresh copies and no quantum memory is retained between blocks. We prove a lower bound matching the upper bound in [arXiv:2510.07788]. Thus the copy complexity of estimating an arbitrary $d$-dimensional state to trace distance $\epsilon$ is, up to absol...

U. Keskin, Jason Luo, Mahbod Majid et al. · 3 citations · ⚡2